Statistical methods for estimating the parameters of a Weibull distribution are developed under the assumption that the available data set is obtained from field performance and is consequently censored on both the left and the right. The extreme lack of data makes estimation very difficult. Estimation equations are defined for both maximum-likelihood and moment based estimates. Simulation results obtained using the defined estimation strategies are not promising but do suggest directions for further study. / Ph. D.

Call number: LD2668 .T4 1978 C56 / Master of Science

Call number: LD2668 .T4 1978 K87 / Master of Science

Call number: LD2668 .T4 1978 L445 / Master of Science

Call number: LD2668 .T4 1979 K37 / Master of Science

No description available.

Thesis (MScEng)--University of Stellenbosch, 2001. / ENGLISH ABSTRACT: First-order second-moment structural reliability methods are used to assess the reliability of a prestressed concrete beam. This beam was designed for imposed office floor loads and partitions following the limit states design method as provided for by the applicable South African structural codes, viz SABS 0100-1:1992 and SABS 0160:1989. The reliability is examined at two limit states. At the ultimate limit state of flexure the ultimate moment of resistance must exceed the applied external moment at the critical section, while at the serviceability limit state of deflection the deflection must satisfy the codespecified deflection criteria. Realistic theoretical models are selected to express the flexural strength and deflection of the prestressed concrete member, while appropriate probabilistic models are gathered from the literature for loading, resistance and modelling uncertainties. The calculated reliability index at the ultimate limit state of flexure (3.10) is lower than expected in view of the fact that this represents a non-critical limit state in the case of a Class 2 prestressed concrete member. This condition can be explained with reference to the relatively high uncertainty associated with the modelling error for flexural strength. The calculated reliability index at the serviceability limit state of deflection (l.67) compares well with acceptable practice. The study further focuses on the sensitivity of the reliability at the two limit states of interest to uncertainty in the various design parameters. The ultimate limit state of flexure is dominated by the uncertainty associated with the modelling error for flexural strength, while the contribution to the overall uncertainty of the ultimate strength and area of the prestressing steel and the effective depth is less significant. In comparison the reliability at the serviceability limit state of deflection is not dominated by the uncertainty associated with a single basic variable. Instead, the uncertainty associated with the modelling error, creep factor and prestress loss factor are all significant. It was also demonstrated that the variability in beam stiffness is not a major source of uncertainty in the case of a Class 2 prestressed concrete member. It is recommended that the present code provisions for ultimate strength and deflection should be reviewed to formulate theoretical models with reduced systematic and random errors. The effect of the uncertainty associated with the creep and prestressed loss factors should also be adressed by adjustment of the partial material factor for concrete at the serviceability limit state of deflection. Furthermore, research must be directed towards formulating an objective failure criterion for deflection. The uncertainty in the deflection limit must therefore be quantified with a probability distribution. / AFRIKAANSE OPSOMMING: Eerste-orde tweede-moment struktuur betroubaarheid metodes word ingespan om die betroubaarheid van 'n voorspanbeton balk te bereken. Hierdie balk is ontwerp vir opgelegte kantoor vloerbelasting en partisies volgens die grenstoestand ontwerp metode soos beskryf in die toepaslike Suid-Afrikaanse boukodes, naamlik SABS 0100-1: 1992 en SABS 0160: 1989. Die betroubaarheid word ondersoek by twee grenstoestande. By die swiglimiet van buiging moet die weerstandsmoment die eksterne aangewende moment oorskrei by die kritieke balksnit, terwyl die defleksie die kriteria soos voorgeskryf deur die kode moet bevredig by die dienslimiet van defleksie. Realistiese teoretiese modelle word gebruik om die buigsterkte en defleksie van die voorspanbeton balk te bereken. Verder is geskikte waarskynlikheid modelle uit die literatuur versamelom die belasting, weerstand en modelonsekerhede te karakteriseer. Die betroubaarheid indeks soos bereken vir die swiglimiet van buiging (3.10) is laer as wat verwag sou word in die lig van die feit dat hierdie nie 'n kritieke grenstoestand verteenwoordig in die geval van 'n Klas 2 voorspan element nie. Dit kan verklaar word met verwysing na die relatiewe groot onsekerheid wat geassosieer word met die modellering fout vir buigsterkte. Die berekende betroubaarheid indeks vir die dienslimiet van defleksie (1.67) vergelyk goed met aanvaarde praktyk. Die studie fokus verder op die sensitiwiteit van die betroubaarheid by die twee grenstoestande onder beskouing ten opsigte van die onsekerheid in die verskillende ontwerp parameters. By die swiglimiet van buiging word die onsekerheid oorheers deur die bydrae van die modelering fout vir buigsterkte. Die bydraes tot die totale onsekerheid deur die swigsterkte en area van die voorspanstaal sowel as die effektiewe diepte is minder belangrik. By die dienslimiet van defleksie word die betroubaarheid nie oorheers deur die onsekerheid van 'n enkele basiese veranderlike nie. In stede hiervan is die onsekerheid van die modellerings fout, kruipfaktor en voorspan verliesfaktor almal noemenswaardig. Daar word verder aangetoon dat die veranderlikheid in balkstyfheid nie 'n belangrike bron van onsekerheid in die geval van 'n Klas 2 voorspan element is nie. Daar word aanbeveel dat die bestaande voorskrifte in die kode vir buigsterkte en defleksie aangespreek moet word deur teoretiese modelle met klein modelonsekerhede te formuleer. Die uitwerking van die onsekerheid van die kruip- en voorspan verliesfaktore kan aangespreek word deur 'n aanpassing te maak in die parsiële materiaalfaktor vir beton in die geval van die dienslimiet van defleksie. Navorsing moet verder daarop gemik wees om 'n objektiewe falingskriterium vir defleksie te formuleer. Die onsekerheid van die toelaatbare defleksie moet dus gekwatifiseer word deur 'n waarskynlikheidsverdeling.

published_or_final_version / Statistics / Doctoral / Doctor of Philosophy

Structural reliability technology provides analytical tools for management of uncertainty in all relevant design factors in structural and mechanical systems. Generally, the goal of analysis is to compute probabilities of failure in structural components or system having single or multiple failure mode. Alternately, modern optimization methods provide efficient numerical algorithms for locating optima, particularly in large-scale systems having prescribed deterministic constraints. Optimization procedure can accommodate random variables either directly in its objective function or as one of the primary constraints. The combination of elementary optimization and probabilistic design techniques is the subject of this study. Presented herein is a general strategy for optimization when the design factors are random variables and some or all of the constraints are probability statements. A literature review has indicated that optimization technology in a reliability context has not been fully explored for the general case of nonlinear performance functions and nonnormal variates associated multiple failure modes. This research focuses upon development of the theory to address this general problem. Because analysis algorithms are complicated, a computer code, program RELOPT, is constructed to automate the analysis. The objective function to be minimized is arbitrary, but would generally be the total expected lifetime costs including all initial costs as well as all costs associated with failure. Uncertainty is assumed to be possible in all design factors (including the factors to be determined), and they are modeled as random variables. In general, all of the constraints can be probability statements. The generalized reduce gradient (GRG) method was used for optimization calculations. Options for point probability calculations are first order reliability analysis using the Rackwitz-Fiessler (R-F) or advanced reliability analysis using Wu/FPI. For system reliability analysis either the first order Cornell's bounds or the second order Ditlevsen's bounds can be specified. Several examples are presented to illustrate the full range of capabilities of RELOPT. The program is validated by checking with independent and exact solutions. An example is provided which demonstrates that the cost of running RELOPT can be substantial as the size of the problem increases.

Metallic structures dominated by tensile loads are vulnerable to fatigue and fracture. Fatigue is produced by oscillatory loads. Quasi-static brittle or ductile fracture can result from a "large" load in the random sequence. Moreover, a fatigue or fracture failure in a member of a redundant structure produces impulsive redistributed loads to the intact members. These transient loads could produce a sequence of failures resulting in progressive collapse of the system. Fatigue and fracture design factors are subject to considerable uncertainty. Therefore, a probabilistic approach, which includes a system reliability assessment, is appropriate for design purposes. But system reliability can be improved by a maintenance program of periodic inspection with repair and/or replacement of damaged members. However, a maintenance program can be expensive. The ultimate goal of the engineer is to specify a design, inspection, and repair strategy to minimize life cycle costs. The fatigue/fracture reliability and maintainability (FRM) process for redundant structure can be a complicated random process. The structural model considered series, parallel, and parallel/series systems of elements. Applied to the system are fatigue loads including mean stress, an extreme load, as well as impulsive loads in parallel member systems. The failure modes are fatigue, brittle and ductile fracture. A refined fatigue model is employed which includes both the crack initiation and propagation phases. The FRM process cannot be solved easily using recently developed advanced structural reliability techniques. A "hybrid" simulation method which combines modified importance sampling (MIS) with inflated stress extrapolation (ISE) is proposed. MIS and ISE methods are developed and demonstrated using numerous examples which include series, parallel and series/parallel systems. Not only reasonable estimates of the probability of system failure but also an estimate of the distribution of time to system failure can be obtained. The time to failure distribution can be used to estimate the reliability function, hazard function, conditional reliability given survival at any time, etc. The demonstration cases illustrate how reliability of a system having given material properties is influenced by the number of series and parallel elements, stress level, mean stress, and various inspection/repair policies.